Wierd Theory Of Mine

[SirNitram]

Alright. The following is wierd, convulted, somewhat sensical, and probably practically useless(That is, there is no practical use for any of this). But I feel like throwing it out.

It's regarding the idea of dimensions. We know, have known for a while, there are three. Height, width, depth. With those, and an anchoring point(All else fails, 'Here' is an anchoring point), we can describe anywhere. Then Einstein came along and included Time as a dimension. Now we can describe anywhere and anywhen.

Now, first, I'm gonna start simple, cause this gets a bit complicated. Each dimension is, effectively, a coordinate set. From one end of the Universe to the other, top to bottum, beginning to end, just a set of points. You get four coordinates, you are describing a time and place. You modify the one for Height, you change your altitude, change the one for Time, you move to a diferent point in existance's history.

One of the problems with this is while we can work out some vague ideas for the conditions to allow time-travel, we can't resolve how it works adequetely. If I go back and modify history, will I shunt into a different universe? With a Timecop made of the Universe itself smack me down?

This is partly Many Worlds theory, partly the mathematical concept of Phase Space, and partly staying up too late watching 'Frequency'. It's kinda hard to explain without a SGI workstation doing the graphics.

Picture a point. That's one dimension. Now a line, that's two. A box is three. A box which changes over time is four. Time for the hard bit. Multiple boxes, which all change over time, but which changes in different ways.

You've just pictured a five dimensional box. Go take a drink, this doesn't get any simpler.

Assuming the fifth dimension is, for want of a better term, probability, we can partially-ressurect Many Worlds(One Universe, but since it's five dimensional, it holds all of it's own possibilities), and easily resolve time travel paradoxs.. It just changes your position on that fifth coordinate.

Quantum particles, which exist in all possibilities, are simply ignoring that fifth coordinate, just like the odd one which changes it's own Time coordinate.

Whew.. I wonder if that made sense to anyone...

[Mr Bean]

Of course execpt try to imagin fith demension phyisics was somthing my friend and I tried to do for fun bact in Middle Schoold(Yes thats right I had very odd friends)

Then agian you can see my own personal theory on multi-unvierses down somewhere on this board called Mat Theory where I went over Multi-demension phyisics and the possibility of traveling to other alternate worlds

[Durandal]

Now, first, I'm gonna start simple, cause this gets a bit complicated. Each dimension is, effectively, a coordinate set.

Correction. Each dimension is a single coordinate in a coordinate set. I guess you could call it a one-coordinate set of coordinates, but that's kind of meaningless. Minor point.

From one end of the Universe to the other, top to bottum, beginning to end, just a set of points. You get four coordinates, you are describing a time and place. You modify the one for Height, you change your altitude, change the one for Time, you move to a diferent point in existance's history.

The universe has no "ends," and you're leaving out one, very crucial element: relativity. All dimensions are relative, so modifying a point's time coordinate will put it in a different time in it's own frame of reference.

One of the problems with this is while we can work out some vague ideas for the conditions to allow time-travel, we can't resolve how it works adequetely. If I go back and modify history, will I shunt into a different universe? With a Timecop made of the Universe itself smack me down?

Relativity is what makes time travel a difficult/impossible concept. According to relativity, there is no preferred frame of reference, so there is no universal timeline. You can't draw out human history on a timeline and simply modify your own time coordinate and land smack-dab in 1955.

This is partly Many Worlds theory, partly the mathematical concept of Phase Space, and partly staying up too late watching 'Frequency'. It's kinda hard to explain without a SGI workstation doing the graphics.

Picture a point. That's one dimension. Now a line, that's two. A box is three. A box which changes over time is four. Time for the hard bit. Multiple boxes, which all change over time, but which changes in different ways.

A point has no dimensions. Have you ever wondered why there's only 1 time dimension and 3 spatial ones? The answer is because there aren't 3 spatial dimensions. All spatial dimensions use the same unit: meters. It's simply cubed to give height, width and depth. Think about it. If I draw a line on a board, can you tell me if that line represents height, width or depth? No. If I draw a rectangular prism, can you tell me how deep it is? What if I rotated it? Does the depth change? No, because there is no depth, width or height. There is merely your perception of them. Keep in mind that this is my personal theory in progress, and I have yet to account for the differences in separate spatial dimensions. For example, if we defined space as one coordinate, we couldn't distinguish between a cube and sphere of equal volume.

However, for the sake of argument, a more accurate description would be...

A point is dimensionless.
A line is 1-dimensional.
A square is 2-dimensional.
A cube is 3-dimensional.

Now, take that cube and put it on a timeline. If the cube exists at any point on that timeline, it is 4-dimensional.

Or, according to my theory...

A point is dimensionless.
A line is 1-dimensional in 1 direction.
A square is 1-dimensional in 2 directions.
A cube is 1-dimensional in 3 directions.

A cube on a timeline is 2-dimensional with 3 spatial directions.

But, remember, that timeline is the cube's timeline, and how quickly that timeline moves is a function of the cube's volume, density and velocity.

Now, if we assume that probability gives time different "directions" (possibilities), then we get really messed up. :)

[SirNitram]

That you for those clarifications, Damien.


I NEED A DRINK!

[Durandal]

Oh, and if you want to get more information about 4-dimensional space (4 spatial coordinates, not 3 and 1 temporal), look for information about manifolds.

[oberon]

If you want to hang onto mathematical definitions and use the term "phase space", then you need a grounding in linear algebra and tensor calculus. Chaos is (partly) the study of ordinary differential equations with (in the phase space) geometry. It uses linear algebra which is extensible to nth-order differential equations. Diffeq and linear algebra are exactly analogous, so once you learn the linear algebra, then you can decompose a system (Fourier, singular value decomposition, blah blah blah) of diffeqs and solve it. Each basis element, or vector, is a coordinate set as Sir Nitram said originally, and you get a different notion of dimension, one that is easy to test for (read: do homework). Then dimension becomes the number of vectors, or to use the better term, basis elements, and each element will have a placeholder for a coordinate label. So in a cartesian frame, you manipulate 3 "3-dimensional" vectors with tensors, which are a special case of matrix (tensors are not matrices but have matrix representation). A tensor is a linear transformation, eg, if you want to shift your coordinate axes, or "anchor" as Sir Nitram called it, then you give the anchor a convenient name such as "zero" or "origin" and manipulate the basis elements (each acting on a different axis) with matrix multiplication by a 3x3 matrix, the tensor that effects the changes--rotations and translations, etc.

I just wanted to point out that there was some apparently unknown background--this kind of thing is discussed in upper-level courses, which seem to resemble philosophy courses more than math. You are encouraged to debate this kind of thing, which is why I always say math is not calculation. The basis, however, is what makes calculus possible.

Example: The Pythagorean theorem works only in a 3-dimensional orthonormal basis, and there you can "Gramm-Schmidt-alize" a system that is not orthonormal in order to compute on it.

Another one: a basis is required to make computations, and linear algebra is important because of the way computers store information in arrays, which are nothing more than vectors of bit-size dimension. Linear algebra is a handy, ubiquitous way to describe the universe, but even more importantly, to perform work on your descriptions. The fact that it's applicable to geometry, diffeq, and computer science, so applicable it actually kinds of melds with all 3, and that it's required for rapid computation (read: technological advancement), speaks to me about spirituality and the existence of God more cogently than any teletubby-addicted moron standing on a virtual soapbox and decrying atheism ever will. Or, in the words of Franklin, "Beer is proof that God exists and he loves us." Oops, I didn't mean to throw in the God stuff at the end. I don't want to turn you off from linear algebra. But do, do convert to linear algebra before you convert to some hokey organized religion.